Über die Hyperfeinstrukturaufspaltung der Mößbauerstrahlung durch zeitlich fluktuierende Magnetfelder

Abstract

In magnetic materials the time fluctuation of the atomic spin causes a fluctuation of the internal magnetic fieldH acting on the nucleus. The Mössbauer radiation in such materials suffers a magnetic hyperfine structure splitting, which displays the field fluctuation in a twofold way: (a) an anomalous line broadening

$$\gamma (m_a m_g ) = (\mu _a m_a /j_a - \mu _g m_g /j_g )^2 \cdot \overline {(H - \bar H)^2 } \cdot \tau _c$$

and (b) an anomalous line displacement

$$\delta (m_a m_g ) = 2(\mu _a m_a /j_a - \mu _g m_g /j_g )^3 \cdot \overline {(H - \bar H)^3 } \cdot \tau _c^{'2} /3.$$

The bar indicates the ensemble average value,μ andm, j are the magnetic moments and the spin quantum numbers of the nucleus in the excited and the ground state.τ _c≈τ ^′ _c are atomic spin correlation times, well known from the treatment of the perturbed angular correlation technique. The presented formulas forγ(m _am_g) andδ(m _am_g) are approximations obtained under the assumptions: (1) the atomic spin Lamor precession is much faster than the Lamor precession of the nucleus, (2) the correlation timeτ _c is not larger than the precession time of the nucleus. In many practical cases both conditions are fulfilled. As an example, the Mössbauer spectrum of Fe NH₄(SO₄)₂· 12H₂O, investigated recently by the Oak Ridge group, is discussed in terms of the presented formulas. A data fit yields the Fe³⁺-spin correlation timesτ _c=2.9·10⁻⁹ sec andτ ^′ _c =2.3·10⁻⁹sec at temperatures ≦4.2°K.